” .. false findings may be the majority or even the vast majority of published research claims” and “… it can be proven that most claimed research findings are false.”
The probability that a a finding is true given that it has been identified as true in the research process.
PPV = \(\frac{(1-\beta)R}{(R+\alpha-R\beta)}\)
a research finding is more likely to be true than false if \((1-\beta)R > \alpha\)
when either the power of the prior probability is very low, the chance that a finding is not due to type 1 error, increases!
let \(u\) be the proportion of samples that would not have been “research findings” but end up being preseneted and reported as such, because of bias.
\(u\) distorts \(\alpha\) and \(\beta\)
PPV decerases with incerasing \(u\) unless \((1-\beta) =< \alpha\)
Conversely, true reseach findings might be annulled due to reverse bias.
PPV = \(R(1 − \beta^n)⁄(R + 1 − (1 − \alpha)^n − R\beta^n)\)
The smaller the studies conducted in a scientific field, the less likely the research findings are to be true.
\(n = 2(\frac{Z_{1-\alpha*0.5} + Z_{1-\beta}}{ES})^2\)
The smaller the effect sizes in a scientific field, the less likely the research findings are to be true.
Decreased PPV with the number of tests
Impact of Bias
Kriegerskorte et al., 2009
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source: https://xkcd.com/1478/
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